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We study critical percolation in hypercubes, revealing convergence properties in limit spaces, indicating significant structural similarities.
We study the connected components in critical percolation on the Hamming hypercube \{0,1\}ᵐ . We show that their sizes rescaled by 2-2m/3 converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled by 2-m/3 and the uniform measure, they converge in distribution with respect to the Gromov–Hausdorff–Prokhorov topology. The two corresponding limits are as in critical Erdős–Rényi graphs.
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Blanc-Renaudie et al. (2026) studied this question.
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